(a) For the circuit shown in Figure 1(a), find the V_in, V_S and power supplied by the dependent source. (10 marks)
(b) Calculate the forward current caused by 0·8 V forward voltage across the diode with ideality factor of semiconductor material as 1

Question

(a) For the circuit shown in Figure 1(a), find the V_in, V_S and power supplied by the dependent source. (10 marks)
(b) Calculate the forward current caused by 0·8 V forward voltage across the diode with ideality factor of semiconductor material as 1. The reverse saturation current of diode is 12·674 × 10⁻¹³ A at a temperature of 22°C. [Assume Boltzmann constant K = 1·38 × 10⁻²³ JK⁻¹, charge of electron q = 1·6 × 10⁻¹⁹ C] (10 marks)
(c) Find the efficiency of a long shunt compound generator rated at 250 kW, 230 V when supplying 75% rated load at rated voltage. The resistances of armature and series field are 0·009 Ω and 0·003 Ω respectively. The shunt field current is 13 A. When the machine is running as a motor at no-load, the armature current is 25 A at rated voltage. (10 marks)
(d) An op-amp circuit is shown in Figure 1(d) below. Assume the op-amp to be ideal. (i) Determine I_1, I_2, I_3 and V_X. (ii) If V_0 is not to be lower than −13 V, calculate the maximum allowed value for R_L. (iii) If R_L is varied in the range 100 Ω to 1 kΩ, what is the corresponding change in I_L and in V_0? (10 marks)
(e) Explain the parity bit generator and parity bit checker. Realize the even parity bit generator and even parity bit checker using X-OR gate. (10 marks)

UPSC Answer Check · Accepted Answer

Solve this multi-part numerical problem by allocating approximately 20% time to each sub-part (a)-(e), with sub-part (d) requiring additional attention for its three sub-sections. Begin with clear circuit diagrams for parts (a) and (d), apply fundamental laws (KCL/KVL, diode equation, generator/motor relations, op-amp virtual ground), show all derivation steps with proper units, and conclude with practical significance of results. For part (e), include truth tables and XOR gate diagrams for parity circuits.
- Part (a): Correct application of KCL/KVL to find V_in, V_S and power from dependent source; identification of controlling variable for dependent source
- Part (b): Accurate calculation of thermal voltage V_T at 22°C (295K), correct substitution in diode equation I = I_s[exp(V/nV_T) - 1] with ideality factor n=1
- Part (c): Proper calculation of armature current, series field drop, and efficiency for long shunt compound generator; correct treatment of no-load motor data for rotational losses
- Part (d)(i)-(iii): Application of ideal op-amp assumptions (virtual short, zero input current); correct nodal analysis for I_1, I_2, I_3, V_X; determination of R_L(max) from saturation limit; analysis of load regulation
- Part (e): Clear explanation of parity generation and checking for error detection; complete realization using XOR gates with proper logic diagrams and truth tables for even parity
- Consistent use of proper units (V, A, Ω, W) and significant figures throughout all numerical calculations
- Clear circuit diagrams for parts (a), (d), and (e) with labeled components and current/voltage polarities
- Physical interpretation of results: power flow direction, diode conduction regime, generator efficiency implications, op-amp operating limits, and parity scheme applications in data communication

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies dependent source type and control in (a); applies Shockley diode equation with proper thermal voltage in (b); distinguishes long shunt vs short shunt in (c); applies ideal op-amp constraints (virtual ground, infinite input impedance) in (d); explains odd/even parity distinction with error detection capability in (e)	Minor conceptual errors such as wrong polarity for dependent source, approximate thermal voltage without calculation, confusion between generator and motor operation, or incomplete parity explanation	Fundamental misconceptions like treating dependent source as independent, using wrong diode equation, applying short shunt formulas to long shunt, ignoring virtual ground concept, or describing parity without XOR logic
Numerical accuracy	20%	10	Precise calculations: V_T = 25.5 mV at 295K, diode current ≈ 0.5 mA range, generator efficiency ~85-90%, correct op-amp currents in mA range, R_L(max) accurate to 2 significant figures; all values with proper units and reasonable engineering precision	Correct method but arithmetic errors or unit conversion mistakes (e.g., kW vs W, mA vs A); final answers within 10% of correct value; inconsistent significant figures	Order of magnitude errors, missing critical terms (e.g., ignoring -1 in diode equation for forward bias), wrong efficiency formula, or answers without units; demonstrates lack of numerical checking
Diagram quality	15%	7.5	Clear hand-drawn or imagined circuit diagrams for (a) and (d) with labeled nodes, reference directions, and component values; neat XOR gate diagrams for (e) with proper ANSI/IEEE symbols; truth tables with clear headers	Diagrams present but poorly labeled, missing reference polarities, or freehand sketches lacking clarity; gate symbols non-standard but recognizable; incomplete truth tables	Missing essential diagrams, incorrect circuit topology, wrong gate symbols, or no visual representation for parity circuits; diagrams that contradict written solution
Step-by-step derivation	25%	12.5	Systematic KCL/KVL equations for (a); explicit V_T calculation before diode equation; clear power flow diagram for generator with all loss components; nodal equations for op-amp circuit; Boolean expressions derived for parity; each step justified with physical reasoning	Some steps skipped or combined without justification; missing intermediate results; correct final answer but unclear how obtained; minimal explanation of algebraic manipulations	Disjointed calculations without logical flow; missing essential steps like thermal voltage calculation; jumps from given data to final answer; no derivation for Boolean expressions in parity circuits
Practical interpretation	20%	10	Interprets dependent source power direction (absorbing/supplying); comments on diode operating point and temperature sensitivity; discusses generator efficiency in context of Indian railway/rural electrification standards; analyzes op-amp saturation limits and load regulation; relates parity to communication error detection (e.g., in ISRO data links)	Brief mention of physical significance without elaboration; generic statements about efficiency or error detection; no connection to real-world applications or engineering trade-offs	Purely mathematical treatment with no physical interpretation; ignores sign conventions for power; no discussion of why results matter practically; treats all parts as abstract exercises

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